Question

How to solve using perfect square x^2-4x-32=0

Answer 1

$Perfect\ square:(a-b)^2=a^2-2ab+b^2\\\\x^2-4x-32=0\ \ \ \ |add\ 32\ to\ both\ sides\\\\x^2-4x=32\\\\x^2-2x\cdot2=32\ \ \ \ |add\ 2^2\ to\ both\ sides\\\\x^2-2x\cdot2+2^2=32+2^2\\\\(x-2)^2=32+4\\\\(x-2)^2=36\iff x-2=-\sqrt{36}\ or\ x-2=\sqrt{36}\\\\x-2=-6\ or\ x-2=6\ \ \ \ |add\ 2\ to\ both\ sides\\\\\boxed{x=-4\ or\ x=8}$